Cryptology ePrint Archive: Report 2000/008

Abstract: We study various applications and variants of Paillier's probabilistic
encryption scheme. First, we propose a threshold variant of the scheme,
and also zero-knowledge protocols for proving that a given ciphertext
encodes a given plaintext, and for verifying multiplication of encrypted values.

We then show how these building blocks can be used for applying the
scheme to efficient electronic voting. This reduces dramatically the work needed to compute the final result of an election, compared to the previously best known schemes. We show how the
basic scheme for a yes/no vote can be easily adapted to casting a
vote for up to $t$ out of $L$ candidates. The same basic building blocks can also be adapted to provide receipt-free elections, under appropriate physical assumptions. The scheme for 1 out of $L$ elections can be optimised such that for a certain range of parameter values, a ballot has size only $O(\log L)$ bits.

Finally, we propose a variant of the encryption scheme, that allows
reducing the expansion factor of Paillier's scheme from 2 to almost 1.